A real-time Grad–Shafranov PDE solver and MIMO controller

Plasma control experiments require enormous computational power to solve large problems with critical time constraints. For tokamak control, the non-linear and constrained Grad–Shafranov equation needs to be solved in real-time with a cycle time of less than 1 ms. A new algorithm for the solution of this equation based on discrete sine transforms and a tridiagonal solver rather than the commonly used cyclic reduction algorithm is presented. Input signals from magnetic probes and flux loops are the constraints for the equation that must be continuously solved to calculate the magnetic equilibrium. A number of novel mathematical ideas were introduced and several generally applicable numerical strategies were developed using LabVIEW graphical dataflow programming to meet the critical timing goals. Benchmarks on CPUs are reported. Furthermore, the design of a MIMO (multiple input and output) controller to demonstrate the possibilities of tokamak position and shape control using graphical dataflow programming is discussed.